Answer:
(c) five raised to the fourth power divided by three raised to the tenth power
Step-by-step explanation:
You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.
Rules of exponentsThe relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
a^-b = 1/a^b
(a^b)^c = a^(bc)
ApplicationThe given expression can be simplified as follows:
[tex](5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}[/tex]
__
Additional comment
We find math expressions easier to understand when they are written using math notation, instead of words.
For #5 - 7, using the given scale factor and center, dilate the following figures and state the new coordinates.
Given: A scale factor of 1/2 and center N of a figure is given.
Required: To dilate the given figure using the given scale factor and center.
Explanation: Dilation is a transformation, used to change the size of the given figure. If the value of dilation>1 then the new figure enlarges. If dilation<1 then the given figure contracts while a dilation=1 means that the new figure is of the same size.
Now here the center is given to be N. And the scaling factor is 1/2.
The coordinates of center N are (3,2). Point M is 2 units left and 4 units down from point N. Hence for dilation of a factor of 1/2, point M' will be 1 unit to the left and 2 units down from point N -
[tex]\begin{gathered} M^{\prime}=(3-1,2-2) \\ M^{\prime}=(2,0) \end{gathered}[/tex]Similarly, point O is 2 units to the right and 6 units down from point N. Hence for dilation of a factor of 1/2, point O' will be 1 unit to the right and 3 units down from point N.
[tex]\begin{gathered} O^{\prime}=(3+1,2-3) \\ =(4,-1) \end{gathered}[/tex]Final Answer: M'=(2,0)
O'=(4,-1)
triangle IJK with vertices I(-9-8),J(-5-6),and K(-7-3) is drawn on the coordinate grid below. what is the area in square units of triangle IJK
Here, we want to calculate the area of the given triangle
Mathematically, the product of the height and base of a triangle divided by 2 gives its area
Now, as we can see the shape, while IJ represents the base, KJ represents the height
We need to calculate the distance between these points before we can get the area of the triangle
To get the distances between the points, we have to use the distance formula
We can proceed with this as follows;
[tex]\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{For IJ} \\ (x_1,y_1)\text{ = (-9,-8)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |IJ|\text{ = }\sqrt[]{(-5+9)^2+(-6+8)^2} \\ |IJ|\text{ = }\sqrt[]{16\text{ + 4}} \\ |IJ|\text{ = }\sqrt[]{20} \\ \\ \text{For KJ} \\ (x_1,y_1)\text{ = (-7,-3)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |KJ|\text{ = }\sqrt[]{(-5+7)^2+(-6+3)^2} \\ |KJ|\text{ = }\sqrt[]{4+9} \\ |KJ|\text{ = }\sqrt[]{13} \end{gathered}[/tex]Thus, we have the area of the triangle as follows;
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ \\ \text{Area = }\frac{1}{2}\times\sqrt[]{20}\times\sqrt[]{13\text{ }}=\frac{\sqrt[]{260}}{2}\text{ = }\frac{2\sqrt[]{65}}{2}\text{ = }\sqrt[]{65\text{ }}\text{ square units} \end{gathered}[/tex]3 + 51 x 1/10 + 9 x 1/100
Answer:
5.49
Step-by-step explanation:
3+ 51= 54
54 x 1/10= 5.4 + 9 x 1/100
5.4 + 0.09=
5.49
John Baxley borrowed $25,000 for one year. He borrowed some at 13% interest and the rest at 50% interest. At the end of the year, he owed $36,000 in interest how much did he borrow at each rate?
The amount borrowed at 13% interest is $20,945.95.
The amount borrowed at 50% interest is $4,054.05.
How much is borrowed at each rate?The first step is to formulate a system of equations:
a + b = $25,000 equation 1
0.13a + 0.5b = (36,000 - 25,000
0.13a + 0.5b =11,000 equation 2
Where:
a = amount borrowed at 13% interest
b = amount borrowed at 50% interest
Take the following steps to determine the value of b:
Multiply equation 1 by 0.13
0.13a + 0.13b = 3,250 equation 3
Subtract equation 3 from equation 2
7,750 = 0.37b
b = $20,945.95
a = $25,000 - $20,945.95 = $4,054.05
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A store and a bank would both charge fees for
Answer:A returned check
Step-by-step explanation:
Answer: D. bouncing a check
Bouncing a check
When a check is deposited in a bank, or when it is written out to a store teller to ultimately deposit in the store bank, the funds are tracing back from an origin bank account. When the check bounces a fee is then charges by both the bank out of which the check is written (for non-sufficient funds) and by the payee. If the payee is a store they will often charge fees that are charged back to them by their bank of deposit."
If Jenna saves $20 buying an item for 40 percent off the regular price, then what were the regular price and the sales price?
Solution
For this case we can create the following proportional rule:
[tex]\frac{20}{100-40}=\frac{x}{100}[/tex]For this case x = original price
Then solving for x we have:
[tex]x=100\cdot\frac{20}{60}=33.33[/tex]Then the original price is 33.33$
Kurt has pulled 15 marbles from a large bag, and 6 of them are brown. What is the experimental probability that the next marble selected from the bag will be brown? Simplify your answer and write it as a fraction or whole number. A. P(brown) = 1/5 B. P(brown) = 2/5 C. P(brown) = 1/2 D. P(brown) = 3/5
total marbles: 15
brown marbles: 6
Probability : brown marbles / total marbles = 6 /15 (simplify) = 2/5
Solve the following equation for a. Be sure to take into account whether a letter is
capitalized or not.
D = Ga +3h³ a
[tex]a=\frac{D}{G+3h^{3}}[/tex]
Looking at the equation, we can see that “a” is a part of both terms. Therefore, we can factor it out. Then we divide to get “a” by itself.
See details:
When Andy Green broke the land speed record, his vehicle was traveling across a flat portion of the desert with a forward velocity of 341.11 m/s. How long would it take him at that velocity to travel 4.500 km?
Answer:
13.192 seconds
Step-by-step explanation:
You want to know the time to travel 4.500 km at a speed of 341.11 m/s.
Travel timeThe relation between time, speed, and distance is ...
time = distance/speed
time = (4500 m)/(341.11 m/s) ≈ 13.192 s
It would take Andy about 13.192 seconds to travel 4.500 km.
__
Additional comment
The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.
One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.
A bag has six balls labeled A, B, C, D, E, and F.
One ball will be randomly picked, and its letter will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of choosing the letter A or C.
If there is more than one element in the set, separate them with commas.
Sample space:
Event of choosing the letter A or C:
Sample space={ A,B,C,D,E,F}
Event of choosing A or C = {A,C}
What is sample space?
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from A or C.
Then the sample space is:
Sample space= {A,C}
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If students recieve a whole numberof pointson every exam item. Can the exam be worth 80 points
Each response includes a thorough explanation of how it was arrived at. The student seemed to have been unsure of which approach to utilize so they hedged their chances by trying both in the hopes that one of them would work. (I don't think it was rewriting that they forgot to cross out; the student presented their response as "it is either X or Y," then in subsequent questions supplied parallel replies depending on whether X or Y was accurate.)
How can I give this question a grade?
Full points given that they provided the correct response
partial marks for being "half-right"?
Or perhaps they didn't get any points since they didn't fully comprehend the issue?
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Graph the function. Then state the domain and range. f(x) = 1/4x-2
The domain and the range of the function f(x) = 1/4x - 2 is the all set of real values
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The function is given as
f(x) = 1/4x - 2
Next, we plot the graph of the function (see attachment)
From the graph, we can see that the graph is a linear graph
This means that the function has a domain and a range of all set of real values
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True or false?
Barriers that keep a business from entering a market can lead to perfect competition.
Answer: true
Step-by-step explanation:
leads to a monopoly
Find the equation of the line whose slope is -3 and which passes through the point (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
We can use the the point slope form of an equation for this:
y - y1 = m (x - x1)
Replace the y1, x1, and m variables with what we were given:
y - (-2) = -3 (x - 5)
Distribute
y + 2 = -3x + 15
Combine like terms
y = -3x + 13
what is 34.49 divided by 0.2 help!!! due friday
Answer:
17.245
Step-by-step explanation:
34.49 divided by 0.2 is 17.245
After many studies, a researcher finds thatthe probability that a word-recognitionprogram correctly interprets a hand-writtenword is 10. How many words out of40 would the researcher expect theprogram to correctly interpret?
Given:
The probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]Find-:
How many words out of 40 would the researcher expect the program to correctly interpret?
Explanation-:
the probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]For 40 world is:
[tex]\begin{gathered} =\frac{9}{10}\times40 \\ \\ =9\times4 \\ \\ =36 \end{gathered}[/tex]So, there are 36 words.
State the adjacent side for the angle marked as x in the picture.
Answer:
Explanation:
In
A rental car company charges $29 per day to rent a car and $0.05 for every mile driven. Santiago wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $100 to spend. What is the maximum number of days that Santiago can rent the car while staying within his budget?
Answer: He can only go 2 days
Step-by-step explanation:
use the graph to determine which the ordered pair is a solution of the equation y equals negative X over 3 - 1
(3, - 2)
1) As the rule of the function has been given to us. Let's find out which point fits in the Solution for:
y=-x/3 -1
As we can see, the y-intercept is b=-1
3) So, (3, - 2) is the solution. Since (3, -2) belongs to the blue line
Checking algebraically
y=-x/3 -1
-2= -3/3 -1
-2 = -2 TRUE!
-
=
Identify the correct box and whisker plot of the given data.
Given the data below.
[tex]\lbrace1,3,5,6,6,7,8,11,12\rbrace[/tex]The median of the data above is the middle number
[tex]median=6[/tex]The first quartile is:
[tex]\begin{gathered} 1,3,5,6 \\ Q1=\frac{3+5}{2}=\frac{8}{2}=4 \end{gathered}[/tex]The third quartile is:
[tex]\begin{gathered} 7,8,11,12 \\ Q3=\frac{8+11}{2}=\frac{19}{2}=9.5 \end{gathered}[/tex]The box and whisker plot for the data is:
The second option is correct.
Let y² = x² + sin(xy). Find using implicit differentiation.
By using implicit differentiation, we get dy/dx=(2x+cos(xy)y)/(-xcos(xy)+2y)
What is implicit differentiation?
Implicit differentiation is the process to finding the derivative of the implicit function.
We have given,
y^2=x^2+sin(xy)
Differentiate with respect to x, and using product rule
2y dy/dx=d/dx(x^2+sin(xy))
2y dy/dx=(dx^2)/dx+(dsin(xy))/dx
2y dy/dx=2x+cos(xy)(d(xy))/dx
2y dy/dx=2x+cos(xy)[y+x dy/dx]
2y dy/dx=2x+ycos(xy)+xcos(xy)dy/dx
2y dy/dx-xcos(xy) dy/dx=2x+ycos(xy)
On simplification, we get
dy/dx=(2x+xcos(xy))/(-xcos(xy)+2y)
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The city is issuing bonds to raise money for a building project. You obtain a $6700 bond that pays 6% interest annually that matures in 8 years. How much interest will you earn?
The interest will earn is 3216
Interest Earned = Amount * Rate of Interest * Time
Interest Earned = 6700*6%*8 = [tex]6700*\frac{6}{100}*8[/tex]
Interest Earned = 3216
Interest Calculator
The term "interest" refers to the additional revenue received by the investor over and above the investment or the additional debt owed by the borrower over and above the amount borrowed. Simple interest and compound interest are the two different kinds of interest. The sorts of interests are covered in further detail in the interest formula. Let's explore the interest formula in further detail and go through several cases.
Interest Formula: What is it?
Simple interest and compound interest are both included in the interest formula. Interest is the cost a borrower pays a lender for a loan. This additional sum, or the interest, must be paid in addition to the loan itself. The Simple Interest Formula and the Compound Interest Formula are both discussed in the interest formula Compound Interest Formula. The interest formula for both is
Simple Interest = P × R × T
Compound Interest = [tex]P(1 + r/n)^{nt}- P[/tex]
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A new model is to be built to serve the towns of Sunnyvale and Gloomington, who’s centers are 6 miles apart. The developers want to locate the mall not more than 3 miles from the center of Sunnyvale and also not more than 5 miles from the center of Gloomington. Drawl a simple map showing Sunnyvale, Gloomington, and all potential locations for the new mall, based on the given information. Be sure to show the scale of your map. Explain how you determine do the possible locations for the mall.
See explanation below
Explanation:
We are told the centres of the two towns are 6miles apart.
This means the distance between Sunnyvale and Gloomington = 6 miles.
We will draw a line with a distance of 6cm to indicate their distance apart.
The two end points of the line will indicate the location of Sunnyvale and Gloomington respectively.
For the developers to locate the mall not more than 3 miles from the center of Sunnyvale, we will draw a circle which has radius of 3cm. This way the mall doesn't exceed 3 miles from Sunnyvale.
For the developers to locate the mall not more than 5 miles from the center of Gloomington, we will draw a circle which has radius of 5cm. This way the mall doesn't exceed 5 miles from Gloomington.
The scale of the drawing will be 1cm represent 1 mile
You can use a compass(drawing tool) to draw the circles. adjusting the legs to suit the measurement of each radius.
The area under the each of the circles are all the possible locations of the map. The location of the new mall cannot go beyond the area under circles but can be within it.
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. 0 Question content area bottom Part 1 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The statement is true. B. The statement is false. The correct statement is enter your response here. (Simplify your answer.)
Based on the given statement of hy⁰ = 0, the answer is B. The statement is false. The correct statement is hy⁰ = 1.
Why is the mathematical statement wrong?The statement given is that hy⁰ = 0. This is false because of the mathematical rule that whenever a number or figure is raised to the power of 0, the result would be that the answer is 1.
For instance:
2 ⁰ = 1
56 ⁰ = 1
8676⁰ = 1
From hy ⁰ = 0, we take the value of y⁰:
y ⁰ = 1
If y ⁰ = 1, then it means that on the right hand side of the statement, we would have the expression h(1).
This therefore means that the equation hy⁰ = 0 is false because h(1) is h and so the correct statement is:
hy ⁰ = 1
Rest of the question is:
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. hyº = 0
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find angle y If the opposite side is 12 and the adjacent side is 11mm
Answer:
answer is 47.49 because tan theta is equals to 12 / 11 which is 1.09091.
So tan-¹(1.09091) = 47.49
2 printing machines of a printing house can complete the printing work of the required number of Excel in Mathematics textbooks in 20 days. After printing the books for 8 days, if 1 more machine was added, in how many days would the remaining work be completed?
The remaining work can be completed in if 2 printing machines of a printing house can complete the printing work in 20 days, After printing the books for 8 days, if 1 more machine was added, is 8 days.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
2 printing machines of a printing house can complete the printing work in 20 days,
After printing the books for 8 days, if 1 more machine was added,
Assume the total work is x,
Calculate the amount of work done in 8 days by both machines as shown below,
The amount of work done in 8 days = x / 20 × 8
The amount of work done in 8 days = 2x / 5
Calculate the remaining work = x - 2x / 5
The remaining work = 3x / 5
Calculate the time taken to complete the remaining work,
Time = (3x / 5) / (3x / 40) = 8 days
Thus, the total time is 16 days.
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Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = –(x – 6)² + 3?
A) The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
B) The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
D) The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.
Answer:
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
Step-by-step explanation:
You want to know what transformations are needed to form g(x) = –(x – 6)² + 3 from f(x) = x².
TransformationsThe function transformations we are typically concerned with are ...
translation horizontally and verticallyscaling horizontally and verticallyreflection across vertical and horizontal linesEach of these has a recognizable influence on the function.
TranslationTranslation by 'h' units to the right and 'k' units up transforms the function to ...
g(x) = f(x -h) +k
ScalingExpanding a graph horizontally by a factor of p and vertically by a factor of q transforms the function to ...
g(x) = q·f(x/p)
ReflectionReflecting a graph horizontally across the y-axis replaces x with -x.
Reflecting a graph vertically across the x-axis replaces f(x) with -f(x).
Given graphComparing g(x) = -(x -6)² +3 to the original f(x) = x², we see that ...
(h, k) = (6, 3)f(x) was replaced by -f(x)This means the graph was shifted right 6 units and up 3 units. The graph was reflected across the x-axis, so the curve opens downward.
Option c, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units. is the correct answer.
What is graph?
In the field of mathematics, a graph is a representation (visual) or diagram that shows the facts or values in an ordered and systematic way.
The relationships between two or more items are frequently represented by the points on a graph.
As given in the question,
[tex]f(x)=x^2[/tex] and [tex]g(x)= -(x-6)^2 + 3[/tex]
Since, [tex]f(x) = x^2[/tex] we are applying the following three rigid transformations on f(x) to obtain g(x):
Reflection around the x-axis in the graph: [tex]f'(x) = -x^2[/tex]Translation in the +x semi-axis in the graph: [tex]f''(x) = -(x-6)^2[/tex]Translation in the +y semi-axis in the graph: [tex]g(x) = -(x-6)^2+3[/tex]Therefore, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
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Can anyone help me with this?
Solve the system. Check the solution.x + y = 8(x=y-3
Answer:
[tex]\begin{gathered} \text{Solution:} \\ (2.5,5.5) \end{gathered}[/tex]Step-by-step explanation:
Given the following system of equations:
[tex]\begin{gathered} x+y=8\text{ (1)} \\ x=y-3\text{ (2)} \end{gathered}[/tex]Since on equation 2, x is already isolated, substitute it into equation 1:
[tex]\begin{gathered} (y-3)+y=8 \\ \end{gathered}[/tex]Solve for y.
[tex]\begin{gathered} 2y=8+3 \\ y=\frac{11}{2}=5.5 \end{gathered}[/tex]Knowing the value of y, plug it into equation (2) and solve for x:
[tex]\begin{gathered} x=y-3 \\ x=5.5-3 \\ x=2.5 \end{gathered}[/tex]Find the value of 12.56 is multiplied by 8.8 and result is divided by 1.57.
Given:
12.56 is multiplied by 8.8 and the result is divided by 1.57.
To find the final result:
First, we multiply 12.56 by 8.8.
We get,
[tex]12.56\times8.8=110.528[/tex]Next, the result 110.528 is divided by 1.57.
So, we get
[tex]\frac{110.528}{1.57}=70.4[/tex]Hence, the answer is 70.4.